Depending on how you interpret “start again”, the answer will be different than the presented solution. If you flip a coin and get the following sequence:

HTHTHTH

the given answer would consider this as two sequences, one after three flips and another after seven flips. The answer changes if you consider this sequence to have “HTH” after three, five and seven flips.

I won’t spoil what the answer is for the different cases, but I will say it isn’t the same!